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Beyond velocity and acceleration: jerk, snap and higher derivatives (2016)

(iopscience.iop.org)
181 points EndXA | 5 comments | 19 Jun 24 10:16 UTC | HN request time: 0.001s | source
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oldandtired ◴[19 Jun 24 12:31 UTC] No.40727644[source]▶
Here in Victoria (Australia), we commonly see road signs stating that "speed kills" whereas the reality is that it is the jerk that kills.
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Gooblebrai ◴[19 Jun 24 12:49 UTC] No.40727787[source]▶
If you want to be pedantic, you could argue that it is the collision that kills.
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samatman ◴[19 Jun 24 21:07 UTC] No.40732382[source]▶
It isn't, though. It's the jerk.

The difference between falling from a height and landing on a trampoline, and landing on concrete from the same height, is that the trampoline smoothly accelerates you to a halt once you collide with it. The concrete does so much more rapidly: that's jerk. Both of these are collisions with the same amount of force behind them.

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1. rcxdude ◴[20 Jun 24 11:56 UTC] No.40737651[source]▶
No, it's the acceleration. The forces are absolutely different between your two examples. The energy is the same, but in one case the energy is dissipated over a longer time, requiring less acceleration and thus force. Jerk and acceleration will tend to be correlated in collisions, but you can construct cases with very high jerk and low acceleration which are just fine and cases with very high acceleration and low jerk which are not at all safe, though the latter case will generally require a lot more energy (fighter jets and rockets, for example).
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2. ◴[20 Jun 24 14:29 UTC] No.40739171[source]▶
3. samatman ◴[20 Jun 24 15:09 UTC] No.40739603[source]▶
Airbags are the most important safety feature in cars. They don't change the rate of acceleration: the car comes to a halt at the same speed, therefore, the person inside does as well.

What they affect is jerk.

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4. rcxdude ◴[20 Jun 24 16:36 UTC] No.40740585[source]▶
No, they absolutely do change the rate at which the person inside stops: most importantly they affect the amount of time it takes for their head to stop moving, by starting to decelerate it before it hits the dashboard (the seatbelts also contribute to this).
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5. samatman ◴[21 Jun 24 18:53 UTC] No.40752486{3}[source]▶
In other words they change the rate of change of the acceleration. We call that derivative jerk. Jerk is responsible for the shockwave which would otherwise rattle the brain around, it's also the chief factor in producing whiplash.